In such a case Gnome’s monitors configuration is stored in the file ~/.config/monitors.xml. The simplest solution is to configure your monitors in your session as you want them, and then copy this config to the gdm user – this is a system user running Gnome’s login screen.
One more note: this is assuming you’re running gdm as a login manager (there are others, they will
be different).
To copy config file you’ll need this two commands:
sudo cp -v ~/.config/monitors.xml /var/lib/gdm/.config/
sudo chown gdm:gdm /var/lib/gdm/.config/monitors.xml
First one does the copying, second changes ownership of the file to the gdm user.
As far as I remember from my testing, after copying the file you can just switch to gdm screen with [Ctrl]+[Alt]+[F1] to see the difference immediately. You can return to your session either by entering your password to unlock the session or by pressing [Ctrl]+[Alt]+[F2] (or sometimes F3, F4… up to F6).
And one more note. There’s a change your monitors.xml contain some settings that gdm doesn’t like. We’ve had such a case here on Ask Fedora. In such a case gdm will just ignore the file you give it.
One of easier solutions is to delete your own monitors.xml, generate new one by going to Gnome’s Control Panel and configuring your monitor’s setup anew – and saving it – and then repeat the commands I’ve given above to copy it to gdm’s config anew. This all should work without logout or rebooting (at least it did for me on Wayland session).